Adam wants to prove the Base Angles Theorem. On which statement or reason did he make a mistake? Also, how can he fix his mistake? Given: Isosceles ΔABC with AB¯¯¯¯¯¯¯¯ ≅AC¯¯¯¯¯¯¯¯ Prove: ∠B ≅∠C Statements Reasons 1. Isosceles ΔABC with AB¯¯¯¯¯¯¯¯ ≅AC¯¯¯¯¯¯¯¯ 1. Given 2. D, midpoint of BC¯¯¯¯¯¯¯¯ , AD¯¯¯¯¯¯¯¯ through points A and D 2. Construction 3. BD¯¯¯¯¯¯¯¯ ≅DC¯¯¯¯¯¯¯¯ 3. Definition of midpoint 4. AD¯¯¯¯¯¯¯¯ ≅AD¯¯¯¯¯¯¯¯ 4. Reflexive property of congruence 5. ΔABD≅ΔACD 5. SAS Congruence Theorem 6. ∠B ≅∠C 6. CPCTC Theorem (1 point) Responses Statement 6 is incorrect. It should say "∠A ≅∠C ." Statement 6 is incorrect. It should say "∠A ≅∠C ." Reason 5 is incorrect. It should say "SSS Congruence Theorem." Reason 5 is incorrect. It should say "SSS Congruence Theorem." Statement 3 has a mistake. It should say "∠BAD ≅∠CAD ." Statement 3 has a mistake. It should say "∠BAD ≅∠CAD ." Reason 3 is incorrect. It should say "Definition of angle bisector

Answer 1

Adam's proof contains an error in Statement 6. He states that ∠B ≅ ∠C as a result of his earlier work, but this is incorrect in the context of the Base Angles Theorem, which specifically states that the angles opposite equal sides in an isosceles triangle are congruent.

The correct conclusion that follows from the congruence of triangles ΔABD and ΔACD (Statement 5) is indeed that the base angles ∠B and ∠C are congruent. Therefore, the correction needed is not in Statement 6 itself; instead, the proper reasoning supporting that conclusion is necessary.

Mistake: Statement 6 is incorrectly stated as the conclusion ∠B ≅ ∠C.

Correction: It is correctly stated, and the proof should continue to justify that by stating the proper sequence of reasoning leading from the triangles' congruence to the conclusion about the angles.

To clarify, Adam can keep Statement 6 as it is and directly link it to the theorem stating that corresponding angles in congruent triangles are congruent via CPCTC (Corresponding Parts of Congruent Triangles are Congruent).

Summary of corrections needed:

• The reasoning in Statement 6 does not need to change regarding the conclusion of angle congruence. It needs to simply clarify that triangle congruence from Statement 5 directly leads to Statement 6 via CPCTC.

Overall, Adam effectively used the correct structure but should ensure the clarity between the triangle congruence and angle congruence results to avoid confusion in his proof.